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%I #18 Oct 13 2017 05:02:54
%S 1,1,1,1,2,2,3,4,5,6,9,10,13,17,21,25,33,39,49,60,73,88,110,130,158,
%T 191,230,273,331,391,468,556,660,779,927,1087,1284,1510,1775,2075,
%U 2438,2842,3323,3872,4510
%N G.f.: 1 + Sum_{n>=1} x^(3*n-2) / Product_{k=1..n} (1-x^k).
%H Roland Bacher, P. De La Harpe, <a href="https://hal.archives-ouvertes.fr/hal-01285685/document">Conjugacy growth series of some infinitely generated groups</a>, hal-01285685v2, 2016.
%F a(n) ~ Pi^2 * exp(Pi*sqrt(2*n/3)) / (12*sqrt(3)*n^2). - _Vaclav Kotesovec_, Oct 13 2017
%t nmax = 50; CoefficientList[Series[1 + Sum[x^(3*k-2)/QPochhammer[x, x, k], {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 13 2017 *)
%t Flatten[{1, Table[PartitionsP[n] - PartitionsP[n-1] - PartitionsP[n-2] + PartitionsP[n-3], {n, 3, 50}]}] (* _Vaclav Kotesovec_, Oct 13 2017 *)
%Y Apart from leading term, essentially identical to A008483.
%K nonn
%O 0,5
%A _N. J. A. Sloane_, Jan 22 2017